Question

Determine and state an equation of the line perpendicular to 5x-4y=10nand passing through point (5,12).

Answer 1

Answer:

4x + 5y = 80

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 5x - 4y = 10 into this form

Subtract 5x from both sides

- 4y = - 5x + 10 ( divide all terms by - 4 )

y = $\frac{5}{4}$ x + $\frac{5}{2}$ ← in slope- intercept form

with slope m = $\frac{5}{4}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$  = - $\frac{1}{\frac{5}{4} }$ = - $\frac{4}{5}$, thus

y = - $\frac{4}{5}$ x + c ← is the partial equation

To find c substitute (5, 12) into the partial equation

12 = - 4 + c ⇒ c = 12 + 4 = 16

y = - $\frac{4}{5}$ x + 16 ← in slope- intercept form

Multiply through by 5

5y = - 4x + 80 ( add 4x to both sides )

4x + 5y = 80 ← in standard form